# Some Results on Polish Groups

@article{Paolini2018SomeRO, title={Some Results on Polish Groups}, author={Gianluca Paolini and S. Shelah}, journal={arXiv: Logic}, year={2018} }

We prove that no quantifier-free formula in the language of group theory can define the $\aleph_1$-half graph in a Polish group, thus generalising some results from [6]. We then pose some questions on the space of groups of automorphisms of a given Borel complete class, and observe that this space must contain at least one uncountable group. Finally, we prove some results on the structure of the group of automorphisms of a locally finite group: firstly, we prove that it is not the case that… Expand

#### References

SHOWING 1-8 OF 8 REFERENCES

Stability of Nilpotent Groups of Class 2 and Prime Exponent

- Mathematics, Computer Science
- J. Symb. Log.
- 1981

THE COMPLEXITY OF TOPOLOGICAL GROUP ISOMORPHISM

- Mathematics, Computer Science
- The Journal of Symbolic Logic
- 2018

Infinite Abelian Groups – Vol. II

- Pure and Applied Mathematics. Vol. 36-II
- 1973